13 papers
On a Diophantine Equation Involving Lucas Numbers
Seyran S. Ibrahimov, Nazim I. Mahmudov
Let L_t denote the t-th Lucas number. We prove that the Diophantine equation L_m^{n+k} + L_m^n = L_r has no solutions in positive integers r, m, n, and k with m >= 2. In the case n…
Explicit representation of solutions to a linear wave equation with time delay
Javad A. Asadzade, Jasarat J. Gasimov, Nazim I. Mahmudov +1
This paper develops an explicit spectral representation for solutions of a one-dimensional linear wave equation with a constant time delay. The model is considered on a bounded int…
Finite-Approximate Solvability of Linear Operator Equations
Nazim I. Mahmudov
We introduce and study the finite-approximate solvability of operator equations \(Lu = h\) in a Hilbert space setting, where a bounded operator \(L \colon U \to H\) is paired with…
Stochastic Maximum Principles and Linear-Quadratic Optimal Control Problems for Fractional Backward Stochastic Evolution Equations in Hilbert Spaces
Javad A. Asadzade, Nazim I. Mahmudov
This paper develops a comprehensive framework for optimal control of systems governed by fractional backward stochastic evolution equations (FBSEEs) in Hilbert spaces. We first est…
Approximate Controllability of Linear Fractional Impulsive Evolution Equations in Hilbert Spaces
Javad A. Asadzade, Nazim I. Mahmudov
This paper investigates the approximate controllability of linear fractional impulsive evolution equations in Hilbert spaces. The system under consideration involves the Caputo fra…
Representation of solutions to continuous and discrete first-order linear matrix equations with delay
Javad A. Asadzade, Nazim I. Mahmudov
In this paper, we study continuous and discrete linear delay systems given respectively by \[ \dot{X}(ξ) = A_0 X(ξ) + X(ξ)A_1 + B_0 X(ξ-Ï) + X(ξ-Ï)B_1 + G(ξ), \] and its di…